Higher June 2022 Paper 3 Q21
21 Ray has nine cards numbered 1 to 9
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Ray takes at random three of these cards.
He works out the sum of the numbers on the three cards and records the result.
Work out the probability that the result is an even number. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{11}{21}\) | P1 | for any product of 3 probabilities of the form \(\dfrac{a}{9} \times \dfrac{b}{8} \times \dfrac{c}{7}\) where \(a \lt 9\), \(b \lt 8\), \(c \lt 7\) |
| P1 | for a product of 3 probabilities giving an even sum, eg E,E,E \(= \dfrac{4}{9} \times \dfrac{3}{8} \times \dfrac{2}{7}\) or E,O,O \(= \dfrac{4}{9} \times \dfrac{5}{8} \times \dfrac{4}{7}\) | |
| P1 | for summing the product of at least three correct triples, eg (E,E,E + E,O,O + O,O,E =) \(\dfrac{4}{9} \times \dfrac{3}{8} \times \dfrac{2}{7} + \dfrac{4}{9} \times \dfrac{5}{8} \times \dfrac{4}{7} + \dfrac{5}{9} \times \dfrac{4}{8} \times \dfrac{4}{7}\) OR \(3\left(\dfrac{4}{9} \times \dfrac{5}{8} \times \dfrac{4}{7}\right)\) | |
| A1 | for \(\dfrac{11}{21}\) oe SCB1 for answer of \(\dfrac{364}{729}\) (replacement) |
Additional guidance
May see fraction with denominator 504
Students who indicate they are using the approach P(even) = 1 – P(odd) should be given credit as appropriate
Accept any equivalent fraction, decimal form 0.52(38...) or percentage form 52(.38…)%